Radius in GD&T Explained
By Lucas Lo | Updated: June 16, 2025
Table of Contents
As a common arc feature in engineering manufacturing, radius is a core parameter in the GD&T system. Its value directly determines the shape accuracy of the part’s surface and its assembly performance.
This article will introduce the definition, marking, and application of radius. Additionally, it will also clarify some concepts that are easily confused with radius.
1. What is Radius?
As a key geometric parameter, the radius specifies the distance from a circle’s center to its circumference, fundamentally defining the circle’s size and shape.
It can also be interpreted as the length of the line segment linking the center to a point on the circle, commonly symbolized by the letter R.
2. Marking Radius in Engineering Drawings
Different from the diameter’s symbol, the radius uses the capital letter R, which directly originates from the first letter of the English word “radius”. Specific rules are as follows:
2.1. Specific Marking Rules
In engineering drawings, the marking of the radius symbol (R) usually needs to be combined with the type of arc feature (two-dimensional arc / three-dimensional spherical surface), dimensional accuracy, and reference association requirements, and is marked in a layered form.
The first row is the type and number of features of circular arcs as well as the dimensions and tolerance bands as follows:
-Symbol: Based on the features of circular arcs, it can be divided into two-dimensional circular arcs and three-dimensional spheres.
Two-dimensional arc: directly labeled R, if not specified, the default is two-dimensional arc.
Three-dimensional spherical: labeled SR (Spherical Radius).
-Quantity: Multiple identical arcs: use “×” to connect the quantity and symbols, e.g. 6×R, indicating 6 arcs of the same radius.
-Basic size: directly label the radius value and unit, e.g. R15mm.
-Tolerance labeling: add the tolerance range after the value, e.g. R10 ± 0.1mm or R8mm +0.05/-0.03.
The second row of datum associations and geometric tolerances is as follows:
-Datum association
Symbol : Apply datum symbols (such as Ⓐ, Ⓑ) to specify the positioning reference of the arc.
Format: Use the datum symbol (e.g., R18mm Ⓐ) after the radius dimension to indicate a circular arc that is positioned with datum A as the center.
Geometric Tolerance (Shape Control)
Roundness/Contour: For controlling the arc’s shape accuracy, incorporate a geometric tolerance frame.
Control Radius (CR): If a smooth contour (no reverse curvature) is required, label CR instead of R, e.g. CR12mm.
2.2. Comparison table of marking examples
Scenario | Labeling Structure | Interpretation |
Single 2D arc | R10mm | A 2D arc with a radius of 10mm, without tolerance or datum requirements. |
Multiple spherical features | 3×SR30mm ±0.03mm | 3 spherical features with a radius of 30mm and a tolerance of ±0.03mm. |
Arc with datum positioning | R15mm Ⓐ | An arc with a radius of 15mm, positioned centered on datum A. |
Smooth contour control | CR20mm | Control of a radius of 20mm, requiring a smooth contour without inflection points. |
3. Applications of Radius
The radius symbol is widely used in fields such as mechanical manufacturing, aerospace, and medical equipment. By precisely controlling the size and shape of arcs, it addresses critical issues such as assembly accuracy, stress distribution, and surface quality. Its core value lies in providing a standardized geometric definition for arc features, ensuring the reliability of parts under complex working conditions.
3.1. Main Functions of Radius Features
Function 1: Assembly accuracy control and stress uniformization. Radius features, such as fillets and spherical surfaces, provide smooth arc contours for components, avoiding stress concentration and ensuring precise fit during assembly.
Function 2: Surface quality optimization and damage prevention. Arc radii eliminate sharp edges at the parts’ peripheries, improving surface finish and preventing scratches to operators or adjacent components.
Function 3: Complex surface generation and fluid dynamics optimization. In aerospace, automotive, and other fields, radius features are used to construct complex surfaces, such as wing transition arcs and engine air ducts, optimizing fluid flow or structural strength.
3.2. Application Scenarios of Radius Features
Radius features are used in industrial fields to optimize part connections, fits, and surface performance. The following are typical application scenarios:
Bolt or screw installation: When machining bolt holes on rough surfaces such as castings, edge burrs and unevenness are eliminated by rounding.
For example, the arc chamfering of bolt holes in an engine block ensures that the bolt heads fit smoothly, avoiding installation tilting or stress concentration caused by surface irregularities and improving the reliability of the connection.
Bearing or bushing installation: The mounting surfaces of bearing housings and bushings often require rounded transitions to ensure alignment accuracy.
For example, rounding the outer ring mounting positions of bearings in a transmission housing prevents bearing tilting, reduces assembly errors, and extends the service life of transmission components.
Sealing surface processing: The edges of the holes in sealing parts such as hydraulic valve blocks and pipe flanges are rounded to provide a smooth support surface for the sealing rings, preventing seal failure due to rough edges.
For instance, rounding the bolt holes of hydraulic pipe flanges ensures uniform compression of the gasket and effectively prevents liquid leakage.
-Structural components and consumer product design: The stress concentration of aerospace structural components is reduced by arc treatment of weight-reducing holes, enhancing the component strength.
For example, the rounded corner design of electronic product shells not only improves aesthetics but also ensures user safety, preventing edge scratches.
4. Radius Processing Guidelines
This section provides a detailed introduction to the standard procedures and key techniques of radius processing, aiming to offer an operational guide for the precise processing of arc features in actual production, ensuring that the radius accuracy and surface quality requirements in the design drawings are met through standardized steps.
4.1. Radius Processing Procedures
Step 1: Choose an appropriate arc machining tool as per the drawing specifications.The tool’s arc radius must be less than or equal to the designed radius. Options include carbide ball nose end mills, diamond-coated tools, or adjustable radius form tools.
Step 2: Firmly clamp the workpiece using a fixture, align the workpiece reference with the machine coordinate system using a dial indicator or tool setter, and mark the arc center or starting point on the workpiece surface.
Step 3: Set the spindle speed, feed rate, and cutting allowance. The spindle speed is typically 30% to 50% lower than that for drilling, the feed rate is controlled at 0.05 to 0.1 mm/r, and a roughing allowance of 0.2 to 0.5 mm is left for finishing.
Step 4: Execute the arc processing. For CNC processing, write G02/G03 arc interpolation programs through CAM software and enable tool radius compensation; for manual processing, feed slowly and uniformly along the arc trajectory, observing the cutting state to avoid overcutting.
Step 5: After processing, use a micrometer, profilometer, or coordinate measuring machine to inspect the arc dimensions and surface roughness. If there are burrs, use fine sandpaper or polishing tools to smooth them, ensuring a smooth and defect-free arc transition.
4.2. Key Techniques for Radius Processing
Tip 1: Before machining, calibrate the coaxiality between the tool and the arc center. For manual alignment, utilize a dial indicator; for CNC systems, activate automatic centering to avoid contour deviations arising from eccentricity.
Tip 2: Select parameters and cooling based on the material. Use cutting oil for steel to reduce speed, air cooling for aluminum to increase speed, and high-pressure cooling and coated tools for high-temperature alloys.
Tip 3: For high-precision scenarios, reduce the feed rate to 0.02 to 0.05 mm/r, use ball-end mills or diamond tools, and perform layer-by-layer milling to ensure surface accuracy.
Tip 4: Set a safety height and spiral down tool path in CNC programming, and measure the depth successively for manual processing to avoid overcutting or undercutting.
Tip 5: Regularly inspect tool wear. For hard materials, use ceramic tools and reduce cutting speed.
Employ trochoidal milling techniques to reduce tool loading and inhibit edge chipping.
Tip 6: For complex arcs, simulate interference avoidance in CAM software first, and monitor the cutting force during processing. Pause and adjust if any abnormalities occur.
5. How to Measure Radius
Radius is in chamfers (R corners), grooves, edges of round holes, and other geometric features. Compared to diameter, radius is more often used to measure local curved or rounded profiles.
We use Radius Gauge, Vernier Caliper, CMM (Coordinate Measuring Machine),Optical Comparator / Vision Measuring System, Contour Measuring Machine (Profilometer) to measure the radius.
5.1. Radius Gauge
A radius gauge is a simple, go/no-go tool made of a set of metal blades with pre-defined radii (e.g., R1 to R25).
It’s used by matching the blade edge to the curve on the part to visually check if the radius is correct.
It is fast and inexpensive, but only gives a rough comparison, not suitable for high-precision needs.
5.2. Vernier Caliper (Geometric Method)
Use the caliper to the chord length and height of height of an arc, then follow the below geometric formula to calculate the radius.
The accuracy depends on manual readings and calculation, not suitable for complex contours or very small radii.
5.3. CMM (Coordinate Measuring Machine)
CMM can provide high-precision radius values along with full geometric data like roundness, center position, and deviation.
It’s ideal for parts with tight tolerance or when inspection reports are needed.
5.4. Optical Comparator / Vision Measuring System
Optical Comparator / Vision Measuring System can project or capture a magnified image of the part’s edge.
Inspect or digitally measure the radius directly from the screen.
For small, transparent, or delicate parts where contact measurement isn’t ideal, Optical Comparator is a good choice. The accuracy is high, and many systems support automatic edge detection for fast results.
5.5. Contour Measuring Machine (Profilometer)
A contour measuring machine traces the surface profile of the part with a stylus and generates a precise curve on screen.
The software then calculates the radius, curvature, and transition zones in great detail.
It is the most accurate method for analyzing complex or blended curves, and is widely used in mold, optics, and die industries. The contour measureing machine is very expensive.
Below is the table about how to choose a Radius measurement method.
| If you want to… | Recommended Method |
| Quickly verify if the radius is present | Radius Gauge |
| Roughly estimate the radius value | Vernier Caliper + Geometric Formula |
| Precisely measure radius size and tolerance | CMM or Optical Comparator |
| Analyze high-precision continuous contour | Profilometer |
An example is given below for a part with a corner radius specified as R2.50 ± 0.05 mm.
| Approach | Tool | Accuracy Requirement | Recommendation Level |
| Quick Check | Radius Gauge (R2.5) | Rough estimate | ⭐⭐ |
| Precision Check | CMM (Coordinate Measuring Machine) | Within ±0.05 mm | ⭐⭐⭐⭐⭐ |
| Optical Inspection | Optical Comparator / Vision System | Small parts / clear edges | ⭐⭐⭐⭐ |
| Complete Surface Analysis | Profilometer (Contour Measuring Machine) | Requires full curvature or transition data | ⭐⭐⭐⭐⭐ |
6. Radius VS Diameter
In fact, radius and diameter are very similar. They are both core geometric parameters describing circular or spherical features and are both defined around the center of the circle or sphere. Their values are directly related, and both require specific symbols in engineering annotations to clarify the feature type.
They are both used to precisely control the dimensional accuracy of parts and are fundamental parameters in CAD modeling, CNC programming, and processing inspection.
6.1. Definition
Radius (R): refers to the fixed distance from the center of the circle to any point on the arc, it is a one-way measurement that determines the degree of curvature of the arc, the smaller the value, the more curved the arc is, e.g., the rounded corners of a cell phone casing, R2mm, enhances the comfort of the grip.
Diameter (⌀): It refers to the length of a bi-directional line segment passing through the center of a circle, with a value of twice the radius (⌀ = 2R), and is often used to describe the overall span of a circular or spherical feature, e.g., ⌀50mm for a bearing hole, which specifies the overall size of the hole .
6.2. On the way of Labeling
Radius: use the letter “R” as a prefix, for example, R10mm represents a circular arc with a radius of 10mm, and the spherical radius is labeled as SR, like SR20mm means that the spherical radius is 20mm.
Diameter: the symbol “⌀” will be added before the numerical value when labeling. “, like ⌀20mm, S⌀40mm (for sphere).
6.3. On the Function and Application Scenario
Radius: mainly used to control the curvature of circular transition, such as the R3mm fillet of the shaft shoulder of mechanical parts, which can reduce the stress concentration and improve the assembly precision; also used to describe the spherical parts, such as the SR32mm radius of the bearing ball.
Diameter: Focuses on determining the overall size of features such as round holes and shaft diameters, influencing the selection of tool diameters. For instance, fabricating a ⌀10mm bolt hole necessitates a drill bit of matching diameter.
Learn more about diameter: Diameter Symbol in Engineering Drawing
7. Other Concepts Easily Confused with Radius
Apart from diameter, there are several other concepts that are easily confused with radius, as detailed below:
7.1. Chamfer
Definition: A chamfer is a linear beveled transition feature formed by the intersection of two planes, typically denoted by “C + numerical value”. Non-45° chamfers require both angle and length specifications (e.g., 2×60°). Its core purpose is to deburr edges, facilitate assembly, or reduce stress concentration through beveled edges.
R is a rounded curve, while a chamfer is a straight, angled surface.
In CNC machining, chamfers often aren’t explicitly called out on drawings because they typically include notes like “BREAK ALL SHARP EDGES AND REMOVE BURRS.” This usually indicates the customer wants small chamfers—such as C0.1, C0.2, or C0.5. Sometimes, the drawing may also include a note like “Unmarked edges to be
In practice, chamfers are wrongly called “R corners,” especially small ones that resemble small-radius arcs (e.g., R1mm). Since both can be milled or ground and serve similar functions like edge treatment, the “R” and “C” symbols are often mixed up, causing mislabeling or incorrect machining in design and production.
7.2. Curvature Radius
Definition: The radius of curvature is a parameter describing the degree of curvature at a point on non-circular curves (e.g., ellipses, parabolas, gear involutes).
It is the reciprocal of the tangent direction change rate at that point, equivalent to the radius of the best-fitting circle approximating the curve locally.
Reason for confusion: The term “radius of curvature” includes “radius,” which can easily be confused with the fixed radius (R) of circular arcs. In engineering notation, it is frequently abbreviated as “R” (e.g., R500mm), mirroring the traditional symbol for radius.
Critically, the former represents a local variable along a curve, whereas the latter denotes a fixed distance from a circle’s center. Despite their fundamental conceptual differences, design conventions often overlook distinctions in naming and notation, leading to misinterpretations.
Curvature radius” is more of a design or modeling term and is rarely used in CNC machining drawings or programming.
8. Conclusion
Radius (R) is a core parameter in engineering manufacturing, precisely controlled through standardized notation and processes, and widely applied. It is essential to distinguish easily confused concepts to promote the development of the precision industry.
Lucas is a technical writer at ECOREPRAP. He has eight years of CNC programming and operating experience, including five-axis programming. He also spent three years in CNC engineering, quoting, design, and project management. Lucas holds an associate degree in mold design and has self-taught knowledge in materials science. He’s a lifelong learner who loves sharing his expertise.
